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Abstract

In this work some asymptotic and other approximate methods for obtaining interval estimates for system reliability from binomial and/or exponential subsystem test data have been developed. The accuracy of these approximations has been assessed by comparison with exact values (sometimes obtained by simulation). Also, other applications of asymptotic techniques are made to the Weibull distribution and to tolerance limits.

In Chapter 2 and Chapter 5, we develop Edgeworth expansions, Cornish and Fisher expansions for percentage points and Saddlepoint expansions for application to the system reliability problem and to tolerance limits.

In Chapter 3, two simple approximate methods have been derived. The first method forms the basis of the Maximus report (1980) and depends on reducing the component test data to equivalent system test data. The second method depends on equating the system posterior mean and variance with the mean and variance of a single beta distribution. The parameters of this beta distribution, so determined, are used in the construction of interval estimates for system reliability.

In addition, in Chapter 4, approximations for the reliability function and for the hazard rate, posterior to censored Weibull life data, are obtained using an asymptotic expansion due to Lindley.

Publication Type:	Thesis (Doctoral)
Subjects:	H Social Sciences > HA Statistics Q Science > QA Mathematics
Departments:	School of Science & Technology > Mathematics School of Science & Technology > School of Science & Technology Doctoral Theses Doctoral Theses

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